Question

evaluate. 10! / 3! 7!​

Answer 1

$10! \div 3! 7! \\ = \frac{10!}{3! 7!} \\ = \frac{10 \times 9 \times 8}{3 \times 2} \\ = 5 \times 3 \times 8 \\ = 120$

Answer 2

10! / (3! 7!​) = 120

Given:

• $\dfrac{10!}{3!7!}$
• 10! / (3! 7!​)

To Find:

• Evaluate

Solution:

• n ! = Product of all the natural numbers from 1 to n  
• n = 1 .2 . 3 . ... (n - 1) . n
• n ! = n ( n - 1) !

Step 1:

10! can be re written as

10 × 9 × 8 × 7 !

Step 2:

Calculate 3!

3 × 2 × 1 = 6

Step 3:

Substitute 10! = 10 × 9 × 8 × 7 !   and  3! = 6  in    $\dfrac{10!}{3!7!}$

$\dfrac{10\times 9\times 8 \times 7!}{6\times 7!}$

Cancel 7! from Numerator and denominator

$\dfrac{10\times 9\times 8 \time }{6 }$

$\dfrac{10\times 72 }{6 }$

= 10 x 12

= 120

Hence, 10! / (3! 7!​) = 120